SOLUTION: Approximate the angle between the two vectors 4i-3j and 4i+3j.
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Question 91469: Approximate the angle between the two vectors 4i-3j and 4i+3j.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To calculate the angle between the vectors 
and 
use this formula:
=\frac{\v{a}\cdot\v{b}}{\left|\v{a}\right|\left|\v{b}\right|})
where 
is the magnitude (ie length) of vector 
and 
is the magnitude (ie length) of vector 
=\frac{4*4+-3*3}{sqrt{4*4+-3*-3}sqrt{4*4+3*3}}=\frac{16+-9}{sqrt{16+9}sqrt{16+9}}=\frac{7}{sqrt{25}sqrt{25}}=\frac{7}{sqrt{625}})
Calculate the dot product in the numerator and the magnitudes in the denominator
So we have this equation:
=\frac{7}{25})
Now take the arccosine of both sides to isolate 
\right)=\cos^{-1}\left(\frac{7}{25}\right))
=\cos^{-1}\left(0.28\left)=1.28700221758657)
So
radians
The angle in degrees is:
*\frac{180}{\pi}=73.739795291688)
So the angle is
degrees
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